Finite Group Databasebeta

← Group #10712387

Character table — Group #10712387

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1122222222222224444444444444444488888888888816161616161616161616161624242424242424242424242424242424
order122223444466688668888888121212122424242444121212122424242424242266668824242424224488881616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111
χ9111-1-1111-1-11-1-1-1-11-11-1ii−i−i111-1-111-1-1i−iii−i−i1-1ii−i−i1-111-1-1i−iii−i−i1-11-1ii−i−iii−i−i11-1-1
χ10111-1-1111-1-11-1-1-1-11-11-1ii−i−i111-1-111-1-1i−iii−i−i1-1ii−i−i1-111-1-1i−iii−i−i-11-11−i−iii−i−iii-1-111
χ11111-1-1111-1-11-1-1-1-11-11-1ii−i−i111-1-111-1-1i−iii−i−i1-1ii−i−i-11-1-111−ii−i−iii1-11-1ii−i−i−i−iii-1-111
χ12111-1-1111-1-11-1-1-1-11-11-1ii−i−i111-1-111-1-1i−iii−i−i1-1ii−i−i-11-1-111−ii−i−iii-11-11−i−iiiii−i−i11-1-1
χ13111-1-1111-1-11-1-1-1-11-11-1−i−iii111-1-111-1-1−ii−i−iii1-1−i−iii1-111-1-1−ii−i−iii1-11-1−i−iii−i−iii11-1-1
χ14111-1-1111-1-11-1-1-1-11-11-1−i−iii111-1-111-1-1−ii−i−iii1-1−i−iii1-111-1-1−ii−i−iii-11-11ii−i−iii−i−i-1-111
χ15111-1-1111-1-11-1-1-1-11-11-1−i−iii111-1-111-1-1−ii−i−iii1-1−i−iii-11-1-111i−iii−i−i1-11-1−i−iiiii−i−i-1-111
χ16111-1-1111-1-11-1-1-1-11-11-1−i−iii111-1-111-1-1−ii−i−iii1-1−i−iii-11-1-111i−iii−i−i-11-11ii−i−i−i−iii11-1-1
χ172222222222222-2-222-2-22222-22222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ182222222222222-2-222-2-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000
χ19222222-2-2-2-22220022002i−2i2i−2i0-2-2-2-20000000000002i−2i2i−2i00000000000000000000−i2i2−i2i22−22−2
χ20222222-2-2-2-22220022002i−2i2i−2i0-2-2-2-20000000000002i−2i2i−2i00000000000000000000i2−i2i2−i2−22−22
χ21222222-2-2-2-2222002200−2i2i−2i2i0-2-2-2-2000000000000−2i2i−2i2i00000000000000000000−i2i2−i2i2−22−22
χ22222222-2-2-2-2222002200−2i2i−2i2i0-2-2-2-2000000000000−2i2i−2i2i00000000000000000000i2−i2i2−i22−22−2
χ2322222-12222-1-1-122-1-12222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10000000000000000
χ2422222-12222-1-1-122-1-12222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-21111-2-211110000000000000000
χ2522222-12222-1-1-122-1-122-2-2-2-22-1-1-1-1-1-1-1-1-2-21111-1-1111122-1-1-1-1-2-211110000000000000000
χ2622222-12222-1-1-122-1-122-2-2-2-22-1-1-1-1-1-1-1-1-2-21111-1-11111-2-2111122-1-1-1-10000000000000000
χ2722222-12222-1-1-1-2-2-1-1-2-22222-2-1-1-1-11111-2-2111111-1-1-1-100−i3i3−i3i300−i3i3−i3i30000000000000000
χ2822222-12222-1-1-1-2-2-1-1-2-22222-2-1-1-1-11111-2-2111111-1-1-1-100i3−i3i3−i300i3−i3i3−i30000000000000000
χ2922222-12222-1-1-1-2-2-1-1-2-2-2-2-2-2-2-1-1-1-1111122-1-1-1-111111100−i3i3−i3i300i3−i3i3−i30000000000000000
χ3022222-12222-1-1-1-2-2-1-1-2-2-2-2-2-2-2-1-1-1-1111122-1-1-1-111111100i3−i3i3−i300−i3i3−i3i30000000000000000
χ31222-2-2222-2-22-2-2222-2-222i2i−2i−2i-222-2-2-2-222−2i2i−2i−2i2i2i-222i2i−2i−2i0000000000000000000000000000
χ32222-2-2222-2-22-2-2222-2-22−2i−2i2i2i-222-2-2-2-2222i−2i2i2i−2i−2i-22−2i−2i2i2i0000000000000000000000000000
χ33222-2-22-2-2222-2-2002-2002-2-220-2-2220000000000002-2-22000000000000000000002−2−22−222−2
χ34222-2-22-2-2222-2-2002-2002-2-220-2-2220000000000002-2-2200000000000000000000−222−22−2−22
χ35222-2-22-2-2222-2-2002-200-222-20-2-222000000000000-222-2000000000000000000002−2−222−2−22
χ36222-2-22-2-2222-2-2002-200-222-20-2-222000000000000-222-200000000000000000000−222−2−222−2
χ37222-2-2-122-2-2-11122-11-222i2i−2i−2i-2-1-11111-1-1−2i2iii−i−i1-1−i−iii00−i3i3i3−i3003−3−330000000000000000
χ38222-2-2-122-2-2-11122-11-222i2i−2i−2i-2-1-11111-1-1−2i2iii−i−i1-1−i−iii00i3−i3−i3i300−333−30000000000000000
χ39222-2-2-122-2-2-11122-11-22−2i−2i2i2i-2-1-11111-1-12i−2i−i−iii1-1ii−i−i00−i3i3i3−i300−333−30000000000000000
χ40222-2-2-122-2-2-11122-11-22−2i−2i2i2i-2-1-11111-1-12i−2i−i−iii1-1ii−i−i00i3−i3−i3i3003−3−330000000000000000
χ41222-2-2-122-2-2-111-2-2-112-22i2i−2i−2i2-1-111-1-1112i−2i−i−iii-11−i−iii2-2-1-1112i−2i−i−iii0000000000000000
χ42222-2-2-122-2-2-111-2-2-112-22i2i−2i−2i2-1-111-1-1112i−2i−i−iii-11−i−iii-2211-1-1−2i2iii−i−i0000000000000000
χ43222-2-2-122-2-2-111-2-2-112-2−2i−2i2i2i2-1-111-1-111−2i2iii−i−i-11ii−i−i2-2-1-111−2i2iii−i−i0000000000000000
χ44222-2-2-122-2-2-111-2-2-112-2−2i−2i2i2i2-1-111-1-111−2i2iii−i−i-11ii−i−i-2211-1-12i−2i−i−iii0000000000000000
χ4522-22-22-222-22-2-222-22-2-200002-22-22-2-2220000002-2000000000000000022-2-2000000000000
χ4622-22-22-222-22-2-222-22-2-200002-22-22-2-2220000002-20000000000000000-2-222000000000000
χ4722-22-22-222-22-2-2-2-2-22220000-2-22-2222-2-2000000-22000000000000000000002i−2i2i−2i00000000
χ4822-22-22-222-22-2-2-2-2-22220000-2-22-2222-2-2000000-2200000000000000000000−2i2i−2i2i00000000
χ4922-2-222-22-2222222-2-22-20000-2-222-22222000000-2-2000000000000000000002-2-2200000000
χ5022-2-222-22-2222222-2-22-20000-2-222-22222000000-2-200000000000000000000-222-200000000
χ5122-2-222-22-22222-2-2-2-2-2200002-222-2-2-2-2-20000002200000000000000002-2-22000000000000
χ5222-2-222-22-22222-2-2-2-2-2200002-222-2-2-2-2-2000000220000000000000000-222-2000000000000
χ5344444-2-4-4-4-4-2-2-200-2-2004i−4i4i−4i02222000000000000−2i2i−2i2i0000000000000000000000000000
χ5444444-2-4-4-4-4-2-2-200-2-200−4i4i−4i4i022220000000000002i−2i2i−2i0000000000000000000000000000
χ55444-4-4-2-4-444-22200-22004-4-44022-2-2000000000000-222-20000000000000000000000000000
χ56444-4-4-2-4-444-22200-2200-444-4022-2-20000000000002-2-220000000000000000000000000000
χ5744-44-444-4-444-4-400-4400000004-44-400000000000000000000000000000000000000000000
χ5844-44-4-24-4-44-222002-20000000-22-2200000023−2323−230000000000000000000000000000000000
χ5944-44-4-24-4-44-222002-20000000-22-22000000−2323−23230000000000000000000000000000000000
χ6044-44-4-2-444-4-222442-2-4-4000042-22-222-2-2000000-2200000000000000000000000000000000
χ6144-44-4-2-444-4-222-4-42-2440000-42-22-2-2-2220000002-200000000000000000000000000000000
χ6244-4-4444-44-444400-4-400000004-4-4400000000000000000000000000000000000000000000
χ6344-4-44-24-44-4-2-2-200220000000-222-2000000−2i32i32i3−2i30000000000000000000000000000000000
χ6444-4-44-24-44-4-2-2-200220000000-222-20000002i3−2i3−2i32i30000000000000000000000000000000000
χ6544-4-44-2-44-44-2-2-244224-40000-42-2-22-2-2-2-20000002200000000000000000000000000000000
χ6644-4-44-2-44-44-2-2-2-4-422-44000042-2-222222000000-2-200000000000000000000000000000000
χ678-800080000-80042−4200000000000000042−420000000000000000000000000000000000000000
χ688-800080000-800−4242000000000000000−42420000000000000000000000000000000000000000
χ698-8000-400004−4i34i342−4200000000000002i6−2i6−22220000000000000000000000000000000000000000
χ708-8000-400004−4i34i3−42420000000000000−2i62i622−220000000000000000000000000000000000000000
χ718-8000-4000044i3−4i342−420000000000000−2i62i6−22220000000000000000000000000000000000000000
χ728-8000-4000044i3−4i3−424200000000000002i6−2i622−220000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).